Exercise 4: (Empirical rule) 1. Recall the empirical Rule. 2. One study, published in 1972 by R. Risebrough, (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443–463). In that study, 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBS, in parts per million (ppm). The PCB concentrations are presented in the following table: 139 166 175 260 204 138 316 396 46 218 173 220 147 216 216 177 246 296 188 89 198 122 250 256 261 132 212 171 164 199 214 177 205 208 320 191 305 230 204 143 175 119 216 185 236 356 289 324 109 265 193 203 214 150 229 236 144 232 87 237 a, Draw the relative frequency histogram using R. b. Isit reasonable to apply the Empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean? c. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean. d. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean. e. Compare your answers in parts (b) and (c).
Exercise 4: (Empirical rule) 1. Recall the empirical Rule. 2. One study, published in 1972 by R. Risebrough, (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443–463). In that study, 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBS, in parts per million (ppm). The PCB concentrations are presented in the following table: 139 166 175 260 204 138 316 396 46 218 173 220 147 216 216 177 246 296 188 89 198 122 250 256 261 132 212 171 164 199 214 177 205 208 320 191 305 230 204 143 175 119 216 185 236 356 289 324 109 265 193 203 214 150 229 236 144 232 87 237 a, Draw the relative frequency histogram using R. b. Isit reasonable to apply the Empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean? c. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean. d. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean. e. Compare your answers in parts (b) and (c).
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ISBN:9781337111348
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Chapter5: A Survey Of Other Common Functions
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Please help me in solving point d and c.
Transcribed Image Text:Exercise 4: (Empirical rule)
1. Recall the empirical Rule.
2. One study, published in 1972 by R. Risebrough, (Proceedings of the 6th Berkeley Symposium on
Mathematics and Statistics, VI, University of California Press, pp. 443–463). In that study, 60 Anacapa
pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and
concentration of PCBS, in parts per million (ppm). The PCB concentrations are presented in the
following table:
139
166
175 260 204
138
316
396
46
218
173
220
147
216
216
177
246
296
188
89
198
122
250
256
261
132
212
171
164
199
214
177
205
208
320
191
305
230
204
143
175
119
216
185
236
356
289
324
109
265
193 203
214
150
229
236
144
232
87
237
a. Draw the relative frequency histogram using R.
b. Is it reasonable to apply the Empirical rule to estimate the percentages of observations that lie within
one, two, and three standard deviations to either side of the mean?
c. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three
standard deviations to either side of the mean.
d. Use the data to obtain the exact percentages of observations that lie within one, two, and three
standard deviations to either side of the mean.
e. Compare your answers in parts (b) and (c).
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